A preposition like with can have pages devoted to it, so it seems rather perverse to focus on one definition and question its applicability to your food scenario.
Among the meanings of with are
"accompanied by" as in pancakes with bacon and eggs
and
"having bits of something (as in an admixture)" as in chocolate chip cookies with walnuts.
You can choose which meaning fits your rice dish better. Are the ingredients side by side or one on top of the other? Stirred up together? You won't know until you see it. If it's take out, probably the latter. If it's in restaurant, perhaps the former.